Granted, the new numbers aren’t much to celebrate. Although unemployment has now fallen to 7.4%, that partly reflects people dropping out of the labor force altogether. The number of actual jobs created, 162,000, fell below expectations and even further below the 189,000 jobs created, on average, each month during the previous year. An adjective many commentators are using to describe July’s job growth is “anemic.”

But none of this is terribly relevant to the specific brief that conservatives have formulated against the new health care law. That argument focuses not on the overall employment level, but rather on large employers’ apparent preference for hiring part-time and temporary workers as opposed to full-time workers.

Walmart, for instance, has increased the percentage of its workforce that’s temporary from 1 to 2% to nearly 10%. Other companies, including Carl’s, Jr. and Hardee’s, have either replaced full-time workers with part-time workers or are threatening to do so, specifically citing as their reason a desire to avoid a 30-hour threshold that would require them either to provide health insurance or pay a $2000-per-employee fine. This requirement, which falls on any company employing more than 50 people, is known as the “employer mandate.”

It’s beyond dispute that part-time and temporary employment are currently higher than they should be, in a healthy recovery, relative to full-time employment. But how much of that can be attributed to businesses’ desire to avoid the employer mandate? There’s much reason to be skeptical that Obamacare is the culprit—not least the simple fact that more than 94% of the companies subject to the employer mandate already provide all their full-time employees with health coverage (though if that coverage fails to meet Obamacare’s minimum coverage and affordability requirements these employers will have to pay a separate fine).

Remember, too, that Obamacare is far from the only challenge employers have on their minds. Georgetown economist Harry Holzer notes “other factors at work such as ongoing uncertainty and the flexibility of [employer] benefits regardless of Obamacare.”

In June, the percentage of so-called “involuntary part-time workers” (i.e., workers forced to take part-time work because they couldn’t get full-time work) jumped from 7.8 million to 8.1 million. Conservative commentators didn’t hesitate to attribute this to Obamacare. “You are now seeing growth in part-time employment in this country while you are seeing a reduction in full-time employment,” said House Majority Leader Eric Cantor. “Employers are beginning to rethink now whether they’re going to be providing a [health care] benefit.”

But on July 2 the Treasury department announced that it would delay the employer mandate, which had originally been set to take effect in 2014, until 2015, apparently to untangle some unexpected difficulties in implementing certain reporting requirements. If employers’ aversion to hiring full-timers really were driven by regulatory minutiae emanating from Washington, D.C., then this reprieve would have removed whatever Sword of Damocles Obamacare had created—not permanently, to be sure, but enough to create a short-term decrease in involuntary part-time employment. And that decrease ought to have shown up in the July jobs report.

But guess what? It didn’t.

Involuntary part-time employment in July was 8.1 million—the same as it was in June. “If we really believe that employers were cutting hours to avoid the sanctions,” the economist Dean Baker, co-director of the Center For Economic and Policy Research, told me via e-mail, ”then there should have been a fall.” A likelier cause than Obamacare for the June uptick in involuntary part-time employment was the furloughing of federal employees due to the budget sequester. The number of temporary workers, meanwhile, continued to increase in July (as it has, incidentally, since before Obamacare was signed into law).

In a recent paper, Baker and Helene Jorgensen of the CEPR argued that if Obamacare were having a significant effect on the hiring of part-time employees, the month to watch would not have been June, but January, since the employer mandate (before its recent postponement) applied to employees hired starting in 2013. (It will now apply to employees hired starting in 2014.) Because hiring varies according to season, Jorgensen and Baker looked at Census data for the first four months of 2013 and compared it with data for the first four months of 2012. They focused on employees who reported working between 26 and 29 hours per week, on the theory that this group was likeliest to be affected by any Obamacare-driven imperative employers felt not to let new hires exceed 30 hours.

The first thing Jorgensen and Baker noticed was that not many workers even fell into this group. They averaged about 853,000—“roughly 0.6% of the labor force.” Remember, too, that fewer than one-third of all part-time employees, even today, are involuntary part-time workers. So the portion of that 26-to-29-hour workforce held below 30 hours at the boss’s cheapskate insistence was probably more like 0.2% of the labor force.

The second thing Jorgensen and Baker noticed was that the number and percentage of employees working 26-to-29 hours (and, by implication, the number and percentage of employees doing so involuntarily) was essentially the same during the first four months of 2013 as it had been during the first four months of 2012. Indeed, it had gone down slightly (though the change was not statistically significant). If the employer mandate bogeyman were affecting employment patterns in any meaningful way, then the number and percentage of 26-to-29-hour part-timers ought to have gone up in 2013.

None of this proves that the employer mandate will never have any affect on employment. We won’t really know whether it does until health reform has been up and running for some time. But the early “evidence” that Obamacare is killing jobs is too weak for anyone with a fact-based curiosity about the matter to take seriously.